限制势的求和规则
Sum rules for Confining Potentials
摘要：
使用格林函数与一维薛定谔方程，它是可能的，建立一个层次的总和规则涉及的本征值的限制势，只有一个boundstate频谱。对于某些势函数，求和规则可能导致发散。它表明，当这种情况发生时，它是可能的检查单独的总和规则所满足的对称限制势的偶数和奇数本征态和减法消除的分歧，并产生一个新的总和规则，这是免费的分歧。该程序说明考虑对称幂律电位和使用的几个例子。通过一个例子证明了Airy函数及其导数的零点服从一个求和规则，并验证了该求和规则的正确性。它还示出了如何的程序可能被推广到建立任意对称限制潜力的总和规则。
英文摘要：
Using the Green's function associated with the one-dimensional Schroedinger equation it is possible to establish a hierarchy of sum rules involving the eigenvalues of confining potentials which have only a boundstate spectrum. For some potentials the sum rules could lead to divergences. It is shown that when this happens it is possible to examine the separate sum rules satisfied by the even and odd eigenstates of a symmetric confining potential and by subtraction cancel the divergences exactly and produce a new sum rule which is free of divergences. The procedure is illustrated by considering symmetric power law potentials and the use of several examples. One of the examples considered shows that the zeros of the Airy function and its derivative obey a sum rule and this sum rule is verified. It is also shown how the procedure may be generalised to establish sum rules for arbitrary symmetric confining potentials.
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